{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bayesian Statistics Made Simple\n",
    "===\n",
    "\n",
    "Code and exercises from my workshop on Bayesian statistics in Python.\n",
    "\n",
    "Copyright 2016 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import math\n",
    "import numpy as np\n",
    "from scipy.special import gamma\n",
    "\n",
    "from thinkbayes2 import Pmf, Suite\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The World Cup Problem\n",
    "\n",
    "We'll use λ to represent the hypothetical goal-scoring rate in goals per game.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute prior probabilities for values of λ, I'll use a Gamma distribution.  \n",
    "\n",
    "The mean is 1.3, which is the average number of goals per team per game in World Cup play."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022562"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Zfclr8yqw1cw2A48CX/Ve3gN4y8xKgCXA6/WFfKKgz7qJN+26uuGb5Wu2se/QcR+rERH5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f763c170450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from thinkbayes2 import MakeGammaPmf\n",
    "\n",
    "xs = np.linspace(0, 8, 101)\n",
    "pmf = MakeGammaPmf(xs, 1.3)\n",
    "thinkplot.Pdf(pmf)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  Write a class called `Soccer` that extends `Suite` and defines `Likelihood`, which should compute the probability of the data (the time between goals in minutes) for a hypothetical goal-scoring rate, `lam`, in goals per game.\n",
    "\n",
    "Hint: For a given value of `lam`, the time between goals is distributed exponentially.\n",
    "\n",
    "Here's an outline to get you started:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Soccer(Suite):\n",
    "    \"\"\"Represents hypotheses about goal-scoring rates.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: scoring rate in goals per game\n",
    "        data: interarrival time in minutes\n",
    "        \"\"\"\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "class Soccer(Suite):\n",
    "    \"\"\"Represents hypotheses about goal-scoring rates.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: scoring rate in goals per game\n",
    "        data: interarrival time in minutes\n",
    "        \"\"\"\n",
    "        x = data / 90\n",
    "        lam = hypo\n",
    "        like = lam * math.exp(-lam * x)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can create a `Soccer` object and initialize it with the prior Pmf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022564"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Zfclr8yqw1cw2A48CX/Ve3gN4y8xKgCXA6/WFfKKgz7qJN+26uuGb5Wu2se/QcR+rERH5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760aefbb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "soccer = Soccer(pmf)\n",
    "thinkplot.Pdf(soccer)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "soccer.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the update after first goal at 11 minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.035267756093734"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BXqkYEreBfnT7/EzLb3M4EhMTQ3LhNDU1TWk642Aiwmc/9gHWnjyyLs3fXniP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\nme02YiV7SQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760ae2f350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(soccer, color='0.7')\n",
    "soccer.Update(11)\n",
    "thinkplot.Pdf(soccer)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "soccer.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the update after the second goal at 23 minutes (the time between first and second goals is 12 minutes).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6029902257702706"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Bb57V6mWKEiHMaxEYeTJoJhlwunjkuZ1W+5rLNpIbomIvycnJpKd7k81NdjcAUFqUzW03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\nYYRJEgghhBEmSSCEEEaYvwFqUFPTHwzKIwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760ab62810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(soccer, color='0.7')\n",
    "soccer.Update(12)\n",
    "thinkplot.Pdf(soccer)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "soccer.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This distribution represents our belief about `lam` after two goals.\n",
    "\n",
    "## Estimating the predictive distribution\n",
    "\n",
    "Now to predict the number of goals in the remaining 67 minutes.  There are two sources of uncertainty:\n",
    "\n",
    "1. We don't know the true value of λ.\n",
    "\n",
    "2. Even if we did we wouldn't know how many goals would be scored.\n",
    "\n",
    "We can quantify both sources of uncertainty at the same time, like this:\n",
    "\n",
    "1. Choose a random values from the posterior distribution of λ.\n",
    "\n",
    "2. Use the chosen value to generate a random number of goals.\n",
    "\n",
    "If we run these steps many times, we can estimate the distribution of goals scored.\n",
    "\n",
    "We can sample a value from the posterior like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.2000000000000002"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lam = soccer.Random()\n",
    "lam"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given `lam`, the number of goals scored in the remaining 67 minutes comes from the Poisson distribution with parameter `lam * t`, with `t` in units of goals.\n",
    "\n",
    "So we can generate a random value like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 67 / 90\n",
    "np.random.poisson(lam * t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we generate a large sample, we can see the shape of the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.8628"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760a9e6cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample = np.random.poisson(lam * t, size=10000)\n",
    "pmf = Pmf(sample)\n",
    "thinkplot.Hist(pmf)\n",
    "thinkplot.Config(xlabel='Goals scored', ylabel='PMF', xlim=[-0.6, 10.5])\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But that's based on a single value of `lam`, so it doesn't take into account both sources of uncertainty.  Instead, we should sample value values from the posterior distribution and generate one prediction for each.\n",
    "\n",
    "**Exercise:** Write a few lines of code to\n",
    "\n",
    "1. Use `Pmf.Sample` to generate a sample with `n=10000` from the posterior distribution `soccer`.\n",
    "\n",
    "2. Use `np.random.poisson` to generate a random number of goals from the Poisson distribution with parameter $\\lambda t$, where `t` is the remaining time in the game (in units of games).\n",
    "\n",
    "3. Plot the distribution of the predicted number of goals, and print its mean.\n",
    "\n",
    "4. What is the probability of scoring 5 or more goals in the remainder of the game?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9466000000000003"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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m/SLe94hhJ3BWkjOA/cAlwNSo2gZ8APh0FyRfq6qnkjw9i77AkQ9OkjR3vQZDVR1MsgHY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\nBxQjCnrnmmWPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760a8f6410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "lams = soccer.Sample(10000)\n",
    "scores = np.random.poisson(lams * t)\n",
    "pmf = Pmf(scores)\n",
    "thinkplot.Hist(pmf)\n",
    "thinkplot.Config(xlabel='Goals scored', ylabel='PMF', xlim=[-0.6, 10.5])\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.087400000000000005"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "sum(scores>=5) / len(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the predictive distribution\n",
    "\n",
    "Alternatively, we can compute the predictive distribution by making a mixture of Poisson distributions.\n",
    "\n",
    "`MakePoissonPmf` makes a Pmf that represents a Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from thinkbayes2 import MakePoissonPmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we assume that `lam` is the mean of the posterior, we can generate a predictive distribution for the number of goals in the remainder of the game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JDTLcJalBs3HjMGmPsPy8i2Z1f6vOnnyXDmn22HOXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760aa86590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam = soccer.Mean()\n",
    "rem_time = 90 - 23\n",
    "lt = lam * rem_time / 90\n",
    "pred = MakePoissonPmf(lt, 10)\n",
    "thinkplot.Hist(pred)\n",
    "thinkplot.Config(title='Option 1', \n",
    "                 xlabel='Expected goals',\n",
    "                 xlim=[-0.5, 10.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictive mean is about 2 goals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9377241975748247"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the chance of scoring 5 more goals is still small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.047208117119541912"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred.ProbGreater(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But that answer is only approximate because it does not take into account our uncertainty about `lam`.\n",
    "\n",
    "The correct method is to compute a weighted mixture of Poisson distributions, one for each possible value of `lam`.\n",
    "\n",
    "The following figure shows the different predictive distributions for the different values of `lam`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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e8YpX4LWvfa2upyMIgrAXlkLclVKo1WpTeeqcn84DnYPBAPl8Ht1uF4lEAqlU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\nRNwFQRCOICLugiAIRxARd0EQhCPI/w/qrY6uvHljbAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760a912dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for lam, prob in soccer.Items():\n",
    "    lt = lam * rem_time / 90\n",
    "    pred = MakePoissonPmf(lt, 14)\n",
    "    thinkplot.Pdf(pred, color='gray', alpha=0.3, linewidth=0.5)\n",
    "\n",
    "thinkplot.Config(xlabel='Expected goals')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute the mixture of these distributions by making a Meta-Pmf that maps from each Poisson Pmf to its probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "metapmf = Pmf()\n",
    "\n",
    "for lam, prob in soccer.Items():\n",
    "    lt = lam * rem_time / 90\n",
    "    pred = MakePoissonPmf(lt, 15)\n",
    "    metapmf[pred] = prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`MakeMixture` takes a Meta-Pmf (a Pmf that contains Pmfs) and returns a single Pmf that represents the weighted mixture of distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MakeMixture(metapmf, label='mix'):\n",
    "    \"\"\"Make a mixture distribution.\n",
    "\n",
    "    Args:\n",
    "      metapmf: Pmf that maps from Pmfs to probs.\n",
    "      label: string label for the new Pmf.\n",
    "\n",
    "    Returns: Pmf object.\n",
    "    \"\"\"\n",
    "    mix = Pmf(label=label)\n",
    "    for pmf, p1 in metapmf.Items():\n",
    "        for x, p2 in pmf.Items():\n",
    "            mix[x] += p1 * p2\n",
    "    return mix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the result for the World Cup problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "mix = MakeMixture(metapmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what the mixture looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760a901290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Hist(mix)\n",
    "thinkplot.Config(title='Option 2', \n",
    "                 xlabel='Expected goals',\n",
    "                 xlim=[-0.5, 10.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Compute the predictive mean and the probability of scoring 5 or more additional goals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.9377505061485507, 0.08565013621838527)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "mix.Mean(), mix.ProbGreater(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
